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Determining the 3D structures of biological molecules is a key problem forboth biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promisingtechnique for structure estimation which relies heavily on computationalmethods to reconstruct 3D structures from 2D images. This paper introduces thechallenging Cryo-EM density estimation problem as a novel application forstochastic optimization techniques. Structure discovery is formulated as MAPestimation in a probabilistic latent-variable model, resulting in anoptimization problem to which an array of seven stochastic optimization methodsare applied. The methods are tested on both real and synthetic data, with somemethods recovering reasonable structures in less than one epoch from a randominitialization. Complex quasi-Newton methods are found to converge more slowlythan simple gradient-based methods, but all stochastic methods are found toconverge to similar optima. This method represents a major improvement overexisting methods as it is significantly faster and is able to converge from arandom initialization.

Microscopic Advances with Large-Scale Learning: Stochastic Optimization for Cryo-EM